Tuesday, October 19, 2010

Sunrise Mystic River Bridge

Moonrise Over East Cambridge

UFO Over Harvard

UFO Over Harvard, October 11, 2010, 6:52pm
Taken from my place looking west.  I might have been shooting through a closed window, not sure.  I didn't notice the "UFO" at the time and it didn't appear in the previous or the next frames, taken at the same place and direction with minutes.  The crescent moon was also near the horizon just outside the frame to the left.  What was it?

Counterfactual Reasoning in Mathematics

In mathematics, we often assume something (not P), show that it leads to a logical contradiction, and then conclude that P is in fact true.  Mathematician Terence Tao has an interesting discussion of proof by contradiction and related techniques in The “no self-defeating object” argument, revisited.